few_shots: Example:
Problem/activity:
You’re mixing ingredients for cookies. The recipe says to combine 6 tablespoons, or ¾ stick, of butter with 1 cup of sugar. You accidentally mix in a whole stick of butter (8 tablespoons) with the cup of sugar. How can you fix this?


Mathematical concept/skill options: 
A. Analyze proportional relationships and use them to solve real-world and mathematical problems.
B. Understand ratio concepts and use ratio reasoning to solve problems.


Thought: This problem focuses on the ratio between two ingredients. Students do not have to analyze proportional relationships in-depth, which is reserved for a higher grade level, but rather use ratios to find missing values.
Answer: B

Now, assign the following problem or activity to one or more relevant mathematical concepts/skills it teaches.
shot_info: fl_problem_000972

6
options: Generate and analyze patterns.

Solve systems of equations.

Create equations that describe numbers or relationships

Use the four operations with whole numbers to solve problems.

Represent and solve problems involving multiplication and division.

Work with addition and subtraction equations.

Represent and solve equations and inequalities graphically.

Rewrite rational expressions.

Multiply and divide within 100.

Add and subtract within 20.

Represent and solve problems involving addition and subtraction.

Understand properties of multiplication and the relationship between multiplication and division.

Understand the connections between proportional relationships, lines, and linear equations.

Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.

Use polynomial identities to solve problems.

Write expressions in equivalent forms to solve problems.

Analyze patterns and relationships.

Perform arithmetic operations on polynomials.

Solve equations and inequalities in one variable.

Interpret the structure of expressions.

Work with radicals and integer exponents.

Understand solving equations as a process of reasoning and explain the reasoning.

Reason about and solve one-variable equations and inequalities.

Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

Write and interpret numerical expressions.

Represent and analyze quantitative relationships between dependent and independent variables.

Gain familiarity with factors and multiples.

Understand the relationship between zeros and factors of polynomials.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Understand and apply properties of operations and the relationship between addition and subtraction.

Use properties of operations to generate equivalent expressions.

Work with equal groups of objects to gain foundations for multiplication.

Solve problems involving the four operations, and identify and explain patterns in arithmetic.

Analyze and solve linear equations and pairs of simultaneous linear equations.
problem_activity: Problem 1
Without solving the systems, explain why the following system must have the same solution.
| System 1:                       $${4x-5y=13 }$$                        $${3x+6y=11}$$ | System 2:                       $${8x-10y=26}$$                        $${x-11y=2}$$ |
|---------------------------------------------------------------------------------------|--------------------------------------------------------------------------------------|
Problem 2
Solve the system of equations by writing a new system that eliminates one of the variables.
$${3x+2y=4}$$
$${4x+7y=1}$$


correct_option_index: 1